Geometrical dynamics of Born-Infeld objects

TL;DR

This paper explores the geometrical dynamics of Dp-branes using the Dirac-Born-Infeld action, revealing simple equations of motion akin to Newton's law, and analyzes their classical Hamiltonian structure within a general relativistic framework.

Contribution

It provides a geometrical approach to Dp-brane dynamics, clarifies the Hamiltonian structure, and examines specific cases like D1-branes in AdS3 x S3 backgrounds.

Findings

Equations of motion resemble Newton's second law.

Identified constraints and their algebra in phase space.

Illustrated dynamics with a D1-brane in AdS3 x S3.

Abstract

We present a geometrical inspired study of the dynamics of $Dp$-branes. We focus on the usual nonpolynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a $D1$-brane immersed in a $AdS_3 \times S^3$ background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation.